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Greer was born to Angela Greer and Reginald Greer. His father fought the Gulf War, and after the war was abusive as a father, locking Greer in a closet as punishment, making him stack bricks only to kick them over, and at one point leaving him in the middle of the city and forcing him to walk home. The former has given him mild claustrophobia. He saved both his mother and father from a house fire after the latter incident. His mother was presumably unharmed in the fire while his father suffered severe burns that left him with scars on one side of his face. When he was in his late teen years his father died of a brain infection while in a Veteran's Hospital. Greer joined the United States Marine Corps after he did not receive an athletic scholarship. He believed that by joining the military he could make a difference. Dr.Nicholas Rush said that Greer was not among the men that he had approved to be on the exploration/military teams that would go through the gate on the Icarus Base after the 9th chevron was dialed. Rush also believed that if not for the military, Greer would have gone to prison, or "worse". (SGU: "Air, Part 3", "Lost")

At the time of the attack on Icarus Base, Greer was awaiting court-martial for assaulting ColonelDavid Telford. He was released by ColonelEverett Young during the attack to help defend the base and evacuated the planet through the Stargate before it exploded. He was the penultimate man to evacuate to Destiny, just ahead of Young. On arrival, he and the rest of the new crew were informed that they were on an unknown spaceship in an unknown region of space, billions of light years from home. When life support systems were failing and Dr.Nicholas Rush thought he had found a solution, Eli Wallace protested, believing that Rush's solution could destroy the ship. Greer held Rush at gunpoint, unwilling to let him make yet another decision that would hurt the Icarus personnel. Lt.Matthew Scott intervened and ordered Greer to lower his weapon, which he did. Rush tried his solution, but it had no affect on anything. When Destiny dropped out of FTL and dialed the Stargate to a planet with the necessary materials to repair the failing life support system, Greer was assigned to the team sent to explore it. He shot Dr.Jeremy Franklin on Rush's orders, as Franklin was about to leave with their only Ancient remote control. Greer then left to find Scott, who was lost in the desert. Greer found Scott and helped get him back to the gate with the Lime needed to fix the life support system. (SGU: "Air, Part 1", "Air, Part 2", "Air, Part 3")

During the lottery, his name was not one of the ones chosen to escape the apparently doomed ship using the Ancient shuttle. When Sgt.Spencer, who was also not chosen, tried to argue that the shuttle could fit more, Greer quickly knocked him out with the butt of his rifle, before things could get out of hand. He chose to remain alone in his quarters for the end, watching the approaching star through his window. (SGU: "Light")

He discovered Sgt.Spencer's corpse when Spencer failed to report for duty. When the investigation eventually led to an informal trial, he suggested the use of force to restore ColonelEverett Young's authority. This idea was turned down by Young himself. After Camile Wray was put in charge, she took him off the active-duty list. Greer believed that she did so out of suspicion that he killed Spencer. She didn't give him a straight answer, though he insisted that they would talk about it further. The situation was resolved when Spencer's death was revealed to be a suicide. (SGU: "Justice")

A day later, the civilian personnel mutinied against the military, sealing them off in one section of the ship. Greer and ColonelEverett Young, using Ancient environmental suits, went onto the hull and reentered the ship on the civlians' side to unseal the doors and retake the ship. Greer was posted in the mess hall with Lt.Vanessa James to keep watch on the civilians. Once the mutiny was dealt with, the civilians were dismissed, though Greer felt that the issue would come up again. (SGU: "Divided")

A week later, Destiny unexpectedly jumped out of FTL in the vicinity of a Uncharted star with a single planet orbiting it. Greer accompanied the first team to visit the planet, and was the first to sample a kiwi-like fruit, despite objections that it could be poisonous. He then spent a month on the planet while the ship navigated around the star, helping to keep relations between the military and civilians amicable in his own unique way. (SGU: "Faith")

A few days later, along with Eli Wallace, Chloe Armstrong and Lt.Matthew Scott, Greer explored a planet with ruins. There Greer was trapped when, after firing at a Giant spider, a section of the tunnel the team was exploring collapsed. The team was stranded when the Destiny jumped to FTL again. The next day, while searching for a way out of the ruins, Chloe believed she had found a map of the tunnel system. When Greer went down another tunnel to check her findings, it collapsed on him, knocking him unconscious. Unable to dig him out, Scott reluctantly left with Eli and Chloe. He awoke later on and managed to dig himself out, but by the time he reached the Stargate his companions had already left. He set up camp by the gate, awaiting rescue, and was tormented by hallucinations of his father. He was eventually rescued by Lt.Vanessa James, who brought him back to the ship, though he was dismayed when Scott, Eli, and Chloe had not been rescued. (SGU: "Human", "Lost")

When several crew members were infected by Alien ticks that induced hallucinations, Greer suffered one of the most dangerous psychotic episodes of all victims. Convinced that Dr.Nicholas Rush and Camile Wray were plotting another mutiny, he hallucinated being ordered to stop them using deadly force, and nearly killed both. (SGU: "Pain")

When Dr.Nicholas Rush had a dream containing residual memories from using the Long-range communication devices in conjunction with ColonelDavid Telford, the subsequent covert operation to, again, swap consciousnesses with Telford (Rush posing as another member of the Destiny expedition) sparked an interrogation on ColonelEverett Young's part. Greer was posted at the entrance to Telford's quarters and given strict orders to not let anybody except Young through. After a verbal confrontation by Young who accused Telford of conspiring with the Lucian Alliance against Stargate Command and expedition, Telford attacked Young. This drew the immediate attention of Greer who flew in and swiftly and brutally beat Telford, inflicting multiple facial wounds. Greer was pulled off of Telford by Lt.Matthew Scott and both of them were ordered out of Telford's quarters.

After receiving authorization from Lt. GeneralJack O'Neill to further the interrogation "by any means necessary", Young saw fit to order Dr.Adam Brody to vent the atmosphere in Telford's room. As the oxygen levels lowered, Young continued to implore Telford to tell them the information they needed to know. Telford refused and suffocated to death (while still inside Rush's body—causing Rush, inside Telford's body, to convulse and suffocate as well), however Telford's suffocation resulted in the breaking of the brainwashing that had been inflicted on him by the Lucian Alliance. As Telford suffocated, Camile Wray and Scott both protested Young's judgment while Greer remained calm and awaited for Young's next move. With the bonds of the brainwashing broken, Telford divulged that the Lucian Alliance was enacting a plan to dial the ninth chevron and board Destiny as they spoke. With defensive options minimal and little time to act, Young assigned Greer to a team with Scott as part of the ships infantry defenses against the Lucian Alliance's unwarranted boarding of Destiny.

With control of Destiny essentially split in half between the expedition and the Lucian Alliance, Greer remained in the Control interface room of Destiny, one of the soldiers who had not been captured by the Alliance. With the radiation bursts from the nearby Binary pulsar system growing more dangerous, Greer and Scott don the Ancient environmental suit and, after a negotiation between Camile Wray and CommanderKiva, pass through Alliance controlled territory of the ship to a hull breach that had been sealed off by the ship's shields. They pass through the hull and go for a space walk in order to locate one of Destiny'sshield emitters in order to adjust it to withstand the next burst of radiation from the pulsar. While Greer and Scott are on their space walk a coup erupts between the expedition and the Alliance, affecting control of the ship's system and compromising Greer and Scott's ability to re-enter Destiny the way they exited. With the help of Eli Wallace, Rush and Brody, Greer and Scott are able to run along the outside of the hull to an airlock in an unexplored area of the ship.

However, they were not able to reach the airlock before the pulsar's next burst of radiation and were presumed dead by Rush and Brody. However, Scott radioed in moments after the burst past, revealing that he and Greer had hid themselves on the underside of the ships hull in order to block the radiation. They then returned to the airlock they were attempting to enter and were let in by Eli. After re-entering Destiny and regrouping with Eli, Chloe Armstrong, Rush and Brody; Scott and Greer decide to go on a reconnaissance mission to assess the condition of the ship's personnel. While they are away a small contingent of Alliance soldiers pinpoints Eli, Chloe, Rush and Brody's location but before any prisoners can be taken Scott and Greer arrive on the scene and kill the Alliance soldiers. They decide to follow Rush's plan of sealing themselves off in the Hydroponics lab, the safest location on Destiny from the radiation burst, and allow the next burst to kill off the remaining Alliance members. Scott and Greer make their way to the infirmary in order to grab Lt.Tamara Johansen and Wray. Unfortunately, the Alliance launches an attack and pins them in the infirmary. Scott radios Rush and tells him to seal the door despite the fact that they aren't with them. Rush's true plan is effective and the threat of death by radiation burst convinces the remaining Alliance forces to surrender control of Destiny back to the expedition. Greer is among the skeleton crew aboard Destiny who welcomes back the expedition that were evacuated off Destiny by the Alliance and was congratulated by Young when he arrived in the Destiny Gate room. (SGU: "Subversion", "Incursion, Part 1", "Incursion, Part 2", "Intervention")

When SenatorMichaels came on board with Dr.Andrew Covel, Covel needed someone to switch with him so Camile Wray volunteered Greer as she believed he needed to use the Long-range communication device which he always refused to do. Greer was ordered by ColonelEverett Young to do so, but was mad at Wray for forcing him to do something he didn't want to do. Upon switching and learning the details of the Lucian Alliance threat, Greer offered his help in dealing with the threat to ColonelDavid Telford, but was refused. When the Alliance Tel'tak crashed into the building, Greer pulled Wray to safety in an office, but had his leg injured by falling debris. After Wray splints his leg, the two hook up with AirmanEvans and try to make their way out of the building, getting a gun and a radio from a dead Airman along the way. After failing to find a way out and learning of the possible Naquadria bomb threat, Wray and Greer decided to try to disarm it themselves, but discovered they were exposed to a fatal dose of radiation in the process. Evans revealed himself to be Lucian Alliance and took Wray hostage, but she broke free and Greer killed him. The two made it into the ship where Wray tried to disarm the bomb, but failed as their radio was jammed by the radiation and they weren't able to get the full instructions from Varro. Wray apologized to him for their differences, explaining that they stemmed from the fact that he was more into action while she was more into talking and the two got a laugh out of the fact that at the point where all they had to do was talk, Wray had nothing to say. After Dr.Nicholas Rush severed the connection, the two met on the Observation deck, worried as nothing had been heard from Earth since their return and they didn't know what had happened to their loved ones. Greer admitted to Wray he missed his mother and was sorry as they weren't on the best of terms because of his joining the military, but Wray comforted him with the fact that his mother probably knew how he cared about her anyway. (SGU: "Alliances")

Greer was one of two possible candidates for a kidney transplant for Dr.Dale Volker and he agreed to be the one to donate the kidney. When Lt.Tamara Johansen needed to take bone marrow from him, he refused to be sedated due to a lack of medicine on board, even though it caused him great pain. When Volker got nervous about the operation and reminised about watching the stars in his backyard, Greer took him to the Destiny garden to look at the stars. With the help of Dr.Amanda Perry, the operation was a success, but Greer developed infections from it. Even though he wasn't supposed to, Greer walked around the ship despite being in a weakened state, but eventually recovered from his infections. (SGU: "Hope", "Seizure")

After recovering, Greer was sent on a mission to a planet where he and Lt.Matthew Scott encountered a Space Deer, but Greer hesitated to kill one. When a predator attacked, Greer hesitated to fire as well, resulting in it attacking the camp and taking Lt.Tamara Johansen and Cpl.Reynolds captive. Greer returned with a rescue team, but his determination to keep after the predator put him at odds with ColonelEverett Young. Eventually Varro, Tasia and the other Lucian Alliance personnel joined the hunt to Greer's displeasure as he didn't trust them. The team fell into a trap and Young and Lt.Vanessa James were hurt while most of the Alliance team was killed and Greer admitted to James his reasons for hesitating so much: he thought he died during the operation even though James figured it was just the effets of the medicine he was under and he didn't want to ever experience that again. After laying an ambush for the creature which killed one, all of the remaining members of the team except Varro and Greer were killed, leaving the two to rescue TJ and Reynolds alone. Greer still didn't trust Varro who compared him to a friend of his who died on a suicide mission, but worked with him. After locating the two thanks to TJ fixing a radio and calling them, Greer had Varro create a distraction while he rescued the two. Even though Greer could've harmed the creature, he chose not to as it was intelligent and willing to let TJ and Reynolds go after recignizing the same about the them and they hooked up with Varro who escaped the creatures unharmed. On the way back to the Gate, the group encountered another space deer and Greer killed it to take it back to the ship for dinner. As a result of this adventure, Varro earned Greer's trust and at Greer's recommendation, Varro was set free and integrated into the crew. (SGU: "The Hunt")

In another alternate timeline he joined ColonelEverett Young's party in an attempt to collect a live Squiggler. However, the team were again attacked; this time Greer was the first to die. (SGU: "Time")

Elderly Greer and Lisa talking, recorded on kino.

In another alternate timeline, instead of choosing to return to Earth with everyone else, Greer volunteered to remain behind on Destiny as part of the group that were staying to complete the mission. When things got too unstable, he and the rest of the volunteers headed through the Stargate too, but like everyone else except for ColonelDavid Telford, didn't make it to Earth and was presumed dead. However, he ended on a planet that he and other survivors called Novus, 2,000 years in the past, eventually marrying Dr.Lisa Park. The two had four sons, three daughters and fifteen grandchildren in total. (SGU: "Twin Destinies", "Common Descent", "Epilogue")

Greer has difficulty trusting people who are not part of the military, such as Dr.Nicholas Rush. Surprisingly, the only civilian that Greer appears to trust to any degree is Eli Wallace, this is likely either because Colonel Young trusts Eli, or because Greer perceives Eli's innocence. At first glance it seems he has anger issues, but he cares about those aboard the ship. Although he is clever and calm during a struggle, he believes that he can only count on other soldiers during combat and has a hard time trusting the non-military personnel. Greer prioritizes survival over comfort, dismissing the awful taste of an alien sweet potato for the simple reason that it will keep them alive. His sense of humor is unusual but good at mediating conflicts when they arise. (SGU: "Air, Part 1", "Air, Part 2", "Air, Part 3", "Time", "Justice", "Faith")